Efforts to improve the achievement gap between low-income children and their more affluent peers has led to the development of classroom interventions and curricula to increase executive functioning (EF) and social-emotional skills (SE), thought to be foundational for learning. The Second Step Early Learning (SSEL) curriculum is a commercially available curriculum designed to improve school readiness by building EF and SE skills. However, although widely used, it has not been widely studied. Modeling SSEL's underlying theory of change, structural equation modeling (SEM) was used to longitudinally examine the effects of the curriculum on low-income preschool children's kindergarten school readiness through the hypothesized mediating role of EF and SE skills in improving pre-academic skills and task behavior in preschool. In a cluster randomized trial, 972 children attending 63 preschool classrooms within 13 low-income Head Start or community preschools were individually tested at the beginning (T1) and end of preschool (T2, n = 836) and followed into kindergarten. Children's average age at T1 was 53 months, with 51% male, 42% Anglo-American, 26% African-American, and 40% Hispanic-American. Children's EF, social skills, pre-literacy/language, and pre-math skills were assessed by trained child assessors blind to study conditions at T1 and T2. Assessors also rated children's task behavior in the testing situation at T1 and T2. School records of children's kindergarten screening scores were obtained on 345 children at T3. It was expected that SSEL would have both direct and indirect effects on kindergarten readiness through improvements in children's SE and EF skills preschool academic skills and on-task behavior. We found no direct effects of SSEL on either pre-academic or on-task behavior outcomes in preschool, nor on later kindergarten readiness. However, SSEL significantly increased EF, and as expected by SSEL's theory of change, growth in EF predicted gains in both pre-academics (particularly pre-math), and on-task behavior in preschool. End-of-year pre-academic skills and on task behavior in turn predicted better kindergarten readiness. Further, SE (although not impacted by SSEL) had direct and indirect effects on kindergarten readiness. Thus, overall, our findings largely support SSEL's theory of change, particularly in relation to EF.